Romney is just taking after his dad who marched with civil rights leaders in Michigan back in the 1960s. At that time the LDS Church was incredibly racist and said that blacks had the "Mark of Cain". I don't really know all the ins and outs of it, but apparently what George Romney did was pretty revolutionary for a Mormon. He was supposed to even meet with MLK Jr., but only didn't because MLK Jr. was in Detroit on a Sunday and Romney observed the Sabbath.
Weirdly enough, Mittens
approval is actually on the rise in Utah. There are still billboards all over I-15 calling for his resignation, but those are all in Utah County and all the smart Utahns stay out of there.
Utah is the most religious state in the union and something like 80% identifying as Mormon. However, this is quickly changing. Younger people are leaving the LDS Church and we have a huge influx of out of state people moving here (like me) and bringing all their ideas with them. Still not enough to swing the balance, but enough to make Salt Lake City fairly liberal. The surrounding area of the valley though is still very much conservative and Utah county is probably 95% Republican, if not more. However, I think Mormons really only vote Republican for two reasons. They're very anti-abortion and they're very pro-second amendment. Seriously, every Mormon I know has a goddamn arsenal in their house and it all stems back to the US government invading Utah back in the 1800s. Most Mormons hate Trump and that's why Evan McMullin had such a strong turn out in Utah in 2016, but until any other party comes forward with an idea to ban abortion, they'll keep voting Republican.
I haven't fully looked at the ballot for Utah yet, but I suspect there will be another candidate like McMullin on there this time around (something like Utah First Party). Given how much Mormons dislike Trump, I could see a third-party candidate actually winning the state, especially if the LDS Church gets behind them. Utah's measly electoral votes won't put a damper on anything, but it would send a strong message.